Determination of the linear equations of position-sensing detectors for small motion measurement systems

Small motion measurement systems are widely used in industry measurement fields to measure small positional/angular motions. These systems usually consist of two parts: a measuring assembly and a reference assembly. The position-sensing detectors (PSDs) are embedded in either measuring assembly or reference assembly to sense the variations of laser light incidence points when there are any small positional/angular motions. To use these systems, it is necessary to determine the linear equations of PSD readings, which relate the six-degrees-of-freedom small positional/angular motions and PSD readings. The purpose of this paper is to derive these equations based on the paraxial raytracing method. Two measurement systems are used as illustrative examples to validate the proposed methodology. The methodology of this study will be useful for system design of PSD-based measurement systems and their applications.     

Measurement of a fiber-end surface profile by use of phase-shifting laser interferometry

We describe a laser interferometric system in which two objectives are used to measure surface profile on a connectorized fiber-end surface. By the use of the proposed illumination design a He-Ne laser as a point light source is transformed to an extended light source, which is beneficial to localize interference fringe pattern near the test surface. To obtain an optimal contrast of the interference fringe pattern, the flat mirror with an adjustable reflection ratio is used to suit different test surfaces. A piezoelectric transducer attached on the reference mirror can move precisely along the optical axis of the objective and permits implementation of four-step phase-shifting interferometry without changing the relative position between the CCD sensor and the test surface. Therefore, an absolutely constant optical magnification can be accurately kept to capture the interference fringe patterns resulting from a combination of light reflected from both the reference flat mirror and the test surface. The experimental result shows that surface profile on a fiber-end with surface features such as a small fiber diameter of 125 microm and a low reflection ratio of less than 4% are measurable. Measurements on a standard calibration ball show that the accuracy of the proposed setup is comparable with that of existing white-light interferometers and stylus profilometers.     

一维PSD定位精度的实验研究

本文根据实验研究测试了一维(二象限)PSD的线性特性,光斑大小和光束倾斜对PSD定位精度的影响,同时分析了其它一些因素的影响。实验表明,1mm直径的He—Ne激光束定位精度2.5μm,光斑越大,倾斜角越大,PSD的定位精度越低。PSD的线性性除与入射光能量有关外,还与后续处理电路有关。     

Methodology for third-order astigmatism compensation in off-axis spherical reflective systems

The main constraint of classical off-axis reflecting systems is the primary astigmatism that has long been a research topic of interest. This astigmatism in off-axis spherical reflective imaging systems can be eliminated by using the proper configuration. These configurations could be derived from the marginal ray fans equation, and they are valid for small angles of incidence. The conditions for the astigmatism compensation in configurations with two and three off-axis mirrors have been derived and analyzed, which have not been reported previously. The expression that defines the conditions for primary astigmatism compensation in a four-mirror system is presented. This shows that the marginal ray fan equation can be used to obtain the condition for astigmatism compensation of a reflective system with any number of mirrors. The developed methodology is verified by ray-tracing analysis of some examples.     

Lidar measurements taken with a large-aperture liquid mirror. 1. Rayleigh-scatter system

A lidar system has been built to measure atmospheric-density fluctuations and the temperature in the upper stratosphere, the mesosphere, and the lower thermosphere, measurements that are important for an understanding of climate and weather phenomena. This lidar system, the Purple Crow Lidar, uses two transmitter beams to obtain atmospheric returns resulting from Rayleigh scattering and sodium-resonance fluorescence. The Rayleigh-scatter transmitter is a Nd:YAG laser that generates 600 mJ/pulse at the second-harmonic frequency, with a 20-Hz pulse-repetition rate. The sodium-resonance-fluorescence transmitter is a Nd:YAG-pumped ring dye laser with a sufficiently narrow bandwidth to measure the line shape of the sodium D(2) line. The receiver is a 2.65-m-diameter liquid-mercury mirror. A container holding the mercury is spun at 10 rpm to produce a parabolic surface of high quality and reflectivity. Test results are presented which demonstrate that the mirror behaves like a conventional glass mirror of the same size. With this mirror, the lidar system's performance is within 10% of theoretical expectations. Furthermore, the liquid mirror has proved itself reliable over a wide range of environmental conditions. The use of such a large mirror presented several engineering challenges involving the passage of light through the system and detector linearity, both of which are critical for accurate retrieval of atmospheric temperatures. These issues and their associated uncertainties are documented in detail. It is shown that the Rayleigh-scatter lidar system can reliably and routinely measure atmospheric-density fluctuations and temperatures at high temporal and spatial resolutions.     

Vibration transducer using an optical cavity comprising birefringent mirrors

We have developed an optical-cavity system comprising birefringent mirrors for a vibration transducer. To obtain a dispersive-shape signal necessary for reading out the information of mirror vibration, we measure the polarization change of the cavity transmission light caused by the natural birefringence appearing on interferential mirrors; this effect is enhanced by the cavity resonance. Since there are no additional polarization-changing elements inside the cavity, we can achieve the high finesse that is indispensable for a highly sensitive vibration measurement. The principle and an experimental demonstration of the system are reported here.     

基于互相关分析的激光自准直小角度测量技术

应用光学自准直原理,选用激光二极管（LD）为光源,位置敏感探测器（PSD）为光电探测器,构建了一种基于互相关分析的激光自准直小角度测量系统.为了提高小角度测量精度,该系统对光源进行正弦调制,利用互相关分析解调出待测小角度信息.根据互相关分析理论,设计了信号处理系统,对影响系统精度的主要因素进行了分析.实现了测量样机,并进行了性能测试实验.实验表明,互相关解调系统有效地抑制了噪声的影响,样机具有较高的二维小角度测量精度和示值稳定性,在±150″范围内,最大非线性误差为0.6″,重复性误差为0.2″,漂移为0.4″/4h.     

Polarization aberrations. 1. Rotationally symmetric optical systems

The polarization in isotropic radially symmetric lens and mirror systems in the paraxial approximation is examined. Polarized aberrations are variations in the phase, amplitude, and polarization state of the electromagnetic field across the exit pupil. Some are dependent on the incident polarization state and some are not. Expressions through fourth order for phase, amplitude, linear diattenuation, and linear retardance aberrations are derived in terms of the chief and marginal ray angles of incidence and the Taylor series expansion coefficients of the Fresnel equations for reflection and transmission at uncoated and thin-film-coated interfaces. Applications to polarization ray tracing are discussed.     

双端差分吸收激光雷达系统

研究和设计了一实验性双端差分吸收激光雷达系统。其光源为一台双波长双脉冲可调谐Cr:LiSAF激光器,利用BBO晶体腔内倍频和腔内调Q技术,实现了二次和三次谐波输出;激光系统的合作目标为远处一平面镜,光源发射光脉冲和信号采集由微机系统控制。该系统用于测量大气中的NO2和SO2的浓度分布。     

Analysis of the receiver response for a noncoaxial lidar system with fiber-optic output

The return signal of a noncoaxial lidar system with fiber-optic output is examined. The dependence of the overlap regions and the overlap factor of the system on the fiber diameter is calculated for several inclination angles between the laser beam and the optical receiver axes. The effect of central obstruction is included and both cases of Gaussian and quasi-Gaussian laser beam profiles are treated. The irradiance spatial distribution on the focal plane of the system is calculated and experimentally determined. Finally, an alignment procedure of the lidar system is described based on the comparison between the range-corrected lidar signal and the range-corrected exponentially attenuated Rayleigh backscattered coefficient.     

Model of the nonlinear operation of a laser with a gaussian mirror

Abstract

In this paper a semi-classical model of the nonlinear operation of a laser is extended to describe a laser with a Gaussian mirror. Modified nonlinear self-consistent equations including transverse and longitudinal field dependence, gain saturation, spatial hole burning and nonlinear dispersion effects are derived. With the help of an energy theorem an approximate solution for steady-state single mode operation is presented, which relates the small signal gain to the output power and the laser system characteristic parameters. The laser output power characteristics are presented for various cavity configurations, especially, revealing an influence of the Gaussian mirror parameter on the power efficiency of the laser.     

非接触大位移动态测量系统设计及实现

提出一种结构轻巧,驱动及处理电路简单,性能良好的非接触大位移动态测量方案．设计以PSD光电位置敏感器件为核心,利用半导体激光器、透镜成像装置组成的测试系统,突破了由于PSD尺寸因素而影响其测量范围的限制;并给出了信号处理电路．实验表明该系统测量范围宽、测量精度高、结构简单．     

Laser-ranging scanning system to observe topographical deformations of volcanoes

We have developed a laser-ranging system to observe the topographical structure of volcanoes. This system can be used to measure the distance to a target by a laser and shows the three-dimensional topographical structure of a volcano with an accuracy of 30 cm. This accuracy is greater than that of a typical laser-ranging system that uses a corner-cube reflector as a target because the reflected light jitters as a result of inclination and unevenness of the target ground surface. However, this laser-ranging system is useful for detecting deformations of topographical features in which placement of a reflector is difficult, such as in volcanic regions.     

Versatile micromirror with a multimovement mode

A 3 x 3 micromirror array has been designed and successfully fabricated by multilayer silicon surface micromaching technology. It is composed of a bottom electrode, a supporting part, and a mirror plate and can modulate both phase and amplitude of incident light. The maximum deflection length along the vertical direction of the mirror plate is 2 microm, and the rotation angles about the Y and X axes are +/-2.3 degrees and +/-1.45 degrees, respectively; one can obtain an even larger deflection by simply increasing the thickness of the sacrificial layers.     

离轴非球面的条纹反射检测技术

条纹反射测量技术具有动态范围大、灵敏度高的特点,通过高精度的系统标定可以获得很高的测量精度。本文研究将条纹反射测量技术应用于离轴非球面反射镜粗抛光阶段的面形检测,使用激光跟踪仪建立检测系统坐标系,然后将相机和显示屏的实测标定数据代入坐标系并在Zemax软件中建立测量装置的理想模型,通过光线追迹得到理想的屏幕像素点位置,采用相移技术可以得到实测时屏幕像素点位置,从而计算得到被测镜面形的斜率误差,最后积分得到检测结果。文中采用该方法对一块SiC离轴非球面镜进行了实测,并与三坐标测量机的结果进行对比,验证了方法的可行性,可用于指导离轴非球面镜粗抛光阶段的加工。     

激光型基准平台的研制

介绍了一种新型的激光型基准平台.该平台运用重力摆技术使光平台在一定范围内达到了自动安平的功能;运用激光在球面镜单根母线上的光学成像原理、光学补偿技术,解决了宽范围正交光平面的聚集问题;输出了两条正交的水平光基准面与垂直光基准面,通过水平旋转机构与支架升降机构实现了两基准面上、下、左、右位置的任意移动,并保持输出信号基本特性不变.     

用位置敏感传感器进行位移测试的技术研究

目的 研究位置敏感传感器在位移测试中的优化应用。方法 从暗电流背景光的角度进行了分析，简化了电路和光路。结果 利用该方法，设计了一套位移测试系统。结论 所设计的系统正确可用，弥补了用位置敏感传感器作位移测试常见的不足。     

First-order gradients of skew rays of axis-symmetrical optical systems

Current commercial software for analysis and design of optical systems use finite difference (FD) approximation methodology to estimate the gradient matrix of a ray with respect to system variables. However, FD estimates are intrinsically inaccurate, subject to gross error when the denominator is excessively small relative to the numerator. We avoid these problems and determine these gradients by the application of Snell's law. We give the background and basics for determining the first-order gradients of skew rays of optical systems, whereby the differential vector of any ray can be estimated by the product of the developed gradient matrix and differential changes of system variables. The most important application is for optical design by use of optimization methods where the merit function is defined as the spot size. FD used for such optimization is slow for large systems and subject to inaccuracy. The presented methodology is shown to be accurate and computationally faster than traditional FD. Two illustrative examples are provided to validate the proposed method.     

Gaussian-reflectivity mirror resonator for a high-power transverse-flow CO2 laser

A Gaussian-reflectivity mirror resonator is proposed to achieve high-quality laser beams. To analyze the laser fields in a Gaussian-reflectivity mirror resonator, the diffraction integral equations of a Gaussian-reflectivity mirror resonator are converted to the finite-sum matrix equations. Consequently, according to the Fox-Li laser self-reproducing principle, we describe the mode fields and their losses in the proposed resonator as eigenvectors and eigenvalues of a transfer matrix. The conclusion can be drawn from the numerical results that, if a Gaussian-reflectivity mirror is adopted for a plano-concave resonator, a fundamental mode can easily be obtained from a transverse-flow CO2 laser and high-quality laser beams can be expected.     

随机振动功率谱再现自适应控制算法研究

为提高电液随机振动实验的控制精度,提出了一种基于Kalman滤波器的随机振动功率谱再现实时自适应控制方法。基于参考谱的信息设计FIR滤波器,通过对白噪声信号的滤波生成时域驱动信号。采用Kalman自适应滤波器实时跟踪振动实验系统的阻抗特性,并基于自适应逆控制方法对系统的输入信号进行滤波修正,使得系统的响应信号能够高精度再现时域驱动信号,进而实现参考谱的高精度再现。功率谱再现实验验证了算法的有效性。